The 19-year-old arrived at Glanford Park for an initial month last week following an impressive spell at Grimsby and made his debut in the defeat at Blackpool.
Logan told the Scunthorpe Telegraph: "I'm happy to be here, and who knows, maybe I'll stay longer than a month.
"It is a month for now, and he (Manchester City coach Derek Fazackerley) just said you never know, if I'm playing well and the manager wants me to stay, I don't see why not.
"It's experience for me and will only be good for me. It's better than playing in Manchester City reserves.
"And it's one division away from the Premier League, which is where I want to be, but I'm happy to play at Championship level for now."